Small aperture acoustic velocity sensor

ABSTRACT

A small aperture acoustic velocity sensor and a method for velocity measurement are disclosed. In one aspect, the disclosed technology uses spatially-shifted sub-arrays for projection and/or hydrophone receipt and cross-correlation of successive pulses to improve correlation and reduce bias. The spatial shift can be created physically by selection of groups of elements or virtually by weighting the contributions of fixed sub-arrays. Spatial modulation can be used to form a projected signal and measured spatial phase of slope across the set of sub-arrays allows correction of both long- and short-term errors. The disclosed technology uses spatial and/or temporal interpolation.

RELATED APPLICATIONS

This application claims priority to U.S. Application No. 62/199,838,filed on Jul. 31, 2015, entitled “SMALL APERTURE ACOUSTIC VELOCITYSENSOR,” which is incorporated herein by reference in its entirety.

BACKGROUND

Field

The disclosed technology relates to underwater acoustic measurementsystems and, more particularly, to a small aperture acoustic velocitysensor (SAAVS).

Description of the Related Technology

Many new applications of Doppler velocity logs and profilers such asautonomous underwater vehicles (UAVs) and remotely operated vehicles(ROVs) have limited space available for acoustic transducers, but couldbenefit from higher-altitude measurements achievable by going to lowerfrequencies than now used in the Doppler velocity logs that fit in them,thus making wider beamwidth necessary. Wider beamwidth would alsoalleviate certain signal-to-noise ratio (SNR) problems that can arisewith narrow acoustic beams at high speeds or in wavy environments. Withpresent Doppler technology, increasing the beamwidth creates problemswith increased bias, reduced correlation, and consequent increasedvelocity standard deviation at any particular speed. The disclosedtechnology overcomes these problems.

Like the disclosed technology, correlation velocity logs (CVLs) also usespatiotemporal correlation, and use a relatively small aperture and lowfrequency. However, CVLs, having only a single acoustic beam, can onlyuse phase to measure one velocity component. They have specular returnsnear nadir that carry little or no information about horizontalvelocity; that information is weighted toward the sides of the acousticbeam where the signal is weaker. The correlation peak of the returnsignal in lag space is relatively wide and the width variesstochastically, giving a relatively noisy and erratic measurement ofhorizontal velocity. CVLs have a very wide beamwidth requiring modelingof bottom backscatter with multiple parameters, can have low signal tonoise ratio and high flow noise due to their cross-correlation ofindividual array elements, and do not make efficient use of theavailable aperture. Certain sidescan sonars, including syntheticaperture sonars (SASs), may employ CVL methods to help navigate vehicletrajectory and attitude during a sequence of pings from which a bottomimage and/or bathymetric map is generated. This use of CVL methodsshares at least some of the disadvantages listed above for CVLs.

Parametric sonar also uses a relatively small aperture and uses arelatively low frequency over most of the acoustic path. It has thedisadvantages of large source level loss due to inefficient non-linearprojector technology, and a difficult design tradeoff in the choice ofinterfering source frequencies between acoustic beam width and powerdensity.

U.S. Pat. No. RE 35,535 discloses a broadband acoustic Doppler currentprofiler (ADCP). U.S. Pat. No. 5,315,562 and U.S. Pat. No. 5,422,860each disclose aspects of correlation velocity logs. U.S. Pat. No.5,808,967 discloses phased arrays. U.S. Pat. No. 7,542,374 discloses,for phased arrays, a method of removing substantially a bias related tothe velocity component orthogonal to the face. U.S. Pat. No. 7,839,720discloses use of coding to remove sidelobe coupling bias in phased arraysystems. U.S. Pat. No. 5,923,617 discloses blazed arrays.

SUMMARY OF CERTAIN INVENTIVE ASPECTS

The system, method, and computer-readable media of the invention eachhave several aspects, no single one of which is solely responsible forits desirable attributes. Without limiting the scope of this invention,some aspects will now be briefly discussed.

One aspect is a method of measuring velocity underwater using anunderwater active sonar system. The system includes a plurality oftransducer arrays, each transducer array including a plurality ofsub-arrays, configured to spatially modulate and project a plurality ofacoustic beams in different directions, receive and spatially demodulatea spatiotemporal pattern of acoustic signals corresponding to echoes ofthe projected acoustic beams from a plurality of scatterers whilepreserving the relative phase relationship of the backscattered acousticsignals. The system further includes a processor configured to separatereceived acoustic signals backscattered from different ones of theprojected acoustic beams, linearly combine the received acoustic signalsover a portion of the transducer arrays, and measure vehicle velocityand/or water velocity components. The method includes locating a bottomsurface for each of the combined acoustic signals. The method furtherincludes selecting data segments in the combined acoustic signalsincluding echoes of the located bottom surface. The method furtherincludes computing auto-correlations of the selected data segments foreach sub-array at zero time lag and at least one other lag at or nearwhich the combined acoustic signal repeats. The method further includescomputing cross-correlations of the selected data segments among thesub-arrays at zero time lag and at least one other lag at or near whichthe combined acoustic signal repeats. The method further includesestimating velocity to resolve phase ambiguity. Estimating velocityincludes computing a correlation coefficient as a function ofinterpolation parameters. Estimating velocity further includes finding apeak of the correlation coefficient with respect to the interpolationparameters. Estimating velocity further includes correcting the peaklocation for bias. Estimating velocity further includes estimating ahorizontal velocity component. Estimating velocity further includesestimating a vertical velocity component. Estimating velocity furtherincludes setting a velocity estimate based on the estimated horizontaland vertical velocity components. The method further includes computingthe velocity at or near an optimal interpolation point. Computingvelocity at or near an optimal interpolation point includes computinginterpolation parameters corresponding to the velocity estimate.Computing velocity at or near an optimal interpolation point furtherincludes calculating a phase at the peak location. Computing velocity ator near an optimal interpolation point further includes refining thevelocity estimate from the phase calculated at the peak location.

In an embodiment, the method further includes applying beamformingprocessing to separate received acoustic signals.

In an embodiment, the method further includes fitting a parametric modelto the amplitude and phase of an interference pattern of the receivedacoustic signals.

Another aspect is a method of method of measuring velocity underwaterusing an underwater active sonar system. The system includes a pluralityof transducer arrays, each transducer array including a plurality ofsub-arrays, configured to spatially modulate and project a plurality ofacoustic beams in different directions, receive and spatially demodulatea spatiotemporal pattern of acoustic signals corresponding to echoes ofthe projected acoustic beams from a plurality of scatterers in the waterwhile preserving the relative phase relationship of the backscatteredacoustic signals. The system further includes a processor configured toseparate received acoustic signals backscattered from different ones ofthe projected acoustic beams, linearly combine the received acousticsignals over a portion of the transducer arrays, and measure vehiclevelocity and/or water velocity components. The method includes locatinga bottom surface for each of the combined acoustic signals. The methodfurther includes selecting data segments in the combined acousticsignals including echoes of the located bottom surface. The methodfurther includes computing auto-correlations of the selected datasegments for each sub-array at zero time lag and at least one other lagat or near which the combined acoustic signal repeats. The methodfurther includes computing cross-correlations of the selected datasegments among the sub-arrays at zero time lag and at least one otherlag at or near which the combined acoustic signal repeats. The methodfurther includes estimating velocity to resolve phase ambiguity. Themethod further includes computing the velocity at or near an optimalinterpolation point.

Another aspect is an underwater active sonar system. The system includesa plurality of transducer arrays configured to spatially modulate andproject a plurality of acoustic beams in different directions, receiveand spatially demodulate a spatiotemporal pattern of acoustic signalscorresponding to echoes of the projected acoustic beams from a pluralityof scatterers in the water while preserving the relative phaserelationship of the backscattered acoustic signals. The system furtherincludes a processor configured to separate received acoustic signalsbackscattered from different ones of the projected acoustic beams,linearly combine the received acoustic signals over a portion of thetransducer arrays, and measure vehicle velocity and/or water velocitycomponents based on the linearly combined signals.

In an embodiment, the processor applies beamforming processing toseparate received acoustic signals. In another embodiment, the processorfits a parametric model to the amplitude and phase of an interferencepattern of the received acoustic signals.

In an embodiment, the processor measures vehicle velocity bybackscattering sound off the bottom surface of a water body. In anotherembodiment, the processor measures vehicle velocity and/or watervelocity by backscattering sound off volume scatterers within a waterbody.

In an embodiment, at least one of the transducer arrays projects a gatedmonotone pulse to produce a narrowband signal. In an embodiment, atleast one of the transducer arrays projects one or more repetitions of aphase-coded or chirped signal to produce a wideband signal.

In an embodiment, the processor is further configured to interpolatereceived acoustic signals, in at least one of time and space, toapproximate bistatic invariance and the Doppler-shifted pulse repetitioninterval.

In an embodiment, the processor uses the phase of a cross-correlationfunction at or near a lag equal to the Doppler-shifted pulse repetitioninterval or an integer multiple of that interval in multiple acousticbeams to measure velocity.

In an embodiment, each of the transducer arrays comprises at least oneof a phased array, an array of phased arrays, a multichannel array, ablazed array, an array of blazed arrays, and a set of pistontransducers. In an embodiment, the shape of each of the transducer arrayis approximately polygonal, a section of a circle, or a section of anoval.

Another aspect is an underwater active sonar system. The system includesa plurality of projection arrays configured to spatially modulate andproject a plurality of acoustic beams in different directions. Thesystem further includes a plurality of hydrophone arrays configured toreceive and spatially demodulate a spatiotemporal pattern of acousticsignals corresponding to echoes of the projected acoustic beams from aplurality of scatterers while preserving the relative phase relationshipof the backscattered acoustic signals from the scatterers. The systemfurther includes a processor configured to separate received acousticsignals backscattered from different ones of the projected acousticbeams, linearly combine the received acoustic signals over a portion ofthe hydrophone arrays, and measure vehicle velocity and/or watervelocity components based on the linearly combined signals.

Another aspect is an underwater active sonar system. The system includesmeans for spatially modulating a plurality of acoustic beams. The systemfurther includes means for projecting the spatially modulated acousticbeams in different directions. The system further includes means forreceiving a spatiotemporal pattern of acoustic signals corresponding tothe echoes of projected acoustic beams from a plurality of scatterers inthe water while preserving the relative phase relationship of thebackscattered acoustic signals. The system further includes means forspatially demodulating the received spatiotemporal pattern of acousticsignals. The system further includes means for separating the receivedacoustic signals backscattered from different ones of the projectedacoustic beams. The system further includes means for linearly combiningthe separated received acoustic signals over a portion of the receivingmeans. The system further includes means for measuring vehicle velocityand/or water velocity components based on the linearly combined signals.

Another aspect is a velocity-measuring device that uses thespatiotemporal pattern of backscattered acoustic signals. In anembodiment, the device includes a plurality of phased arrays to measurethe spatiotemporal pattern. In an embodiment, the device includes aplurality of non-overlapping sub-arrays to measure the spatiotemporalpattern. In an embodiment, the device uses spatial modulation of anarray to produced one or more acoustic beams at an angle to the normalto the array face.

Another aspect is a correlation velocity log with other than a verticalprojected acoustic beam. In an embodiment, multiple slanted acousticbeams are projected simultaneously, sequentially, two-at-a time, orone-at-a-time. The projector(s) can be a phased array, an array ofphased arrays, a multichannel array of individual elements, amultichannel array with one channel per stave, a blazed array, an arrayof blazed arrays, or a set of piston transducers. The hydrophone(s) canbe the same transducers as the projector(s) or an independent set oftransducers, such as an array of phased arrays, an array of switchablesub-elements, a multichannel array of individual elements, an array ofblazed arrays, or multiple piston transducers. The hydrophone(s) canreceive the echo return signal from a particular acoustic beam at anytime and in any sequence relative to the projection of other acousticbeams and to the projection of similar pulses from the same acousticbeam. The velocity processing hardware and algorithm can either attemptto separate signals from individual acoustic beams or else measure andfit a model to the interference pattern created by the returns frommultiple acoustic beams.

Another aspect relates to a correlation velocity log that uses phaseinformation detecting motion along the acoustic beam axis of each of twoor more acoustic beams to precisely measure two or three components ofvelocity.

Another aspect relates to a correlation velocity log that uses spatialmodulation across an array to create an interference pattern across thecorrelation function in lag space, creating distinct small-scalefeatures that can be more easily tracked to measure horizontal velocitythan the broad smooth shape of the correlation function created by mostCVLs.

Another aspect relates to a correlation velocity log for whichcorrelations are done between combinations of signals from sub-arrays ofelements rather than individual elements. The SNR is higher when signalsare combined linearly before the non-linear cross- or auto-correlationstep. Also, the correlation coefficient is higher when interpolation isperformed before the non-linear correlation step, at least conceptuallyif not in order of completion of execution.

Another aspect relates to a Doppler velocity log for which correlationsare done with a lag in both space and time, not in time alone.

Another aspect relates to a Doppler velocity log for which the spatiallag for each acoustic beam approximates that necessary to ensure thatthe bistatic invariance condition holds when projected along with thevelocity vector onto the plane perpendicular to the acoustic beam axis.

Another aspect uses interpolation to create a virtual spatial and/ortime shift at a spatial and/or time lag other than those at whichmeasurements are made. Designing phased array transducers with selectiveswitching of sub-arrays is difficult for both projection and receipt ofacoustic signals for various practical reasons. Use of interpolationbetween independent adjacent portions of the phased array to create avirtual spatial sub-array shift when the full array is used forprojection can give performance almost as good as when cross-correlatingsignals from overlapping physical sub-arrays.

Embodiments of the disclosed technology measure vehicle velocity in deepwater. Other embodiments are configured for current profiling witheither uniform or non-uniform depth cell sizes. Embodiments of thedisclosed technology use echoes received between multiple pulses (oftenreferred to as pulse-coherent or pulse-to-pulse coherent mode) or echoesreceived after the projected transmission is complete. Embodiments ofthe disclosed technology can project single or multiple gated sinewaves, repeated phase codes or chirps with or without gaps, or any otherrepeated transmissions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating the first step in athree-step introduction to the theory of operation of the disclosedtechnology.

FIG. 2 is a schematic diagram illustrating the second step in thethree-step introduction to the theory of operation of the disclosedtechnology.

FIG. 3 is a schematic diagram illustrating the third step in thethree-step introduction to the theory of operation of the disclosedtechnology.

FIG. 4 is a diagram illustrating the projection of the velocity vectorand hydrophone displacement onto the plane perpendicular to the axis ofan acoustic beam, as well as illustrating the bistatic invarianceprinciple.

FIG. 5 is a diagram of a grid of four rectangular receive sub-arraysthat cover the full aperture of the transmit array of a small apertureacoustic velocity sensor according to an embodiment of the disclosedtechnology.

FIG. 6 is a diagram of a grid of two rectangular receive sub-arrays thatcover the full aperture of the transmit array of a small apertureacoustic velocity sensor according to an embodiment of the disclosedtechnology.

FIG. 7 is a diagram of a grid of four approximately hexagonal receivesub-arrays, aligned with the two center sub-arrays abutting, that coverthe full aperture of the transmit array of a small aperture acousticvelocity sensor according to an embodiment of the disclosed technology.

FIG. 8 is a diagram of a grid of four approximately hexagonal receivesub-arrays, rotated by an amount to fit a rectangular surface, thatcover the full aperture of the transmit array of a small apertureacoustic velocity sensor according to an embodiment of the disclosedtechnology.

FIG. 9 is a diagram of a grid of four approximately hexagonal receivesub-arrays, aligned such that there is a hole in the center, that coverthe full aperture of the transmit array of a small aperture acousticvelocity sensor according to an embodiment of the disclosed technology.

FIG. 10 is a diagram of a grid of four approximately quarter-circlereceive sub-arrays that cover the full aperture of the transmit array ofa small aperture acoustic velocity sensor according to an embodiment ofthe disclosed technology.

FIG. 11 is a diagram of a grid of four rectangular receive sub-arrays,composed of elements that are rotated by an amount, that cover the fullaperture of the transmit array of a small aperture acoustic velocitysensor according to an embodiment of the disclosed technology.

FIG. 12 is a diagram of a small aperture acoustic velocity sensor systemcomposed of four rectangular sub-arrays, a waterproof housing, amounting plate, and an end-cap electrical connector according to anembodiment of the disclosed technology.

FIG. 13 is a block diagram of an exemplary embodiment of the electronicsfor a small aperture acoustic velocity sensor.

FIG. 14 is a flowchart of a process for measuring velocity according toan embodiment of the disclosed technology.

FIG. 15 is a flowchart of a process for the last two steps of FIG. 14 inmore detail for the particular case of a single interpolation dimensionaligned with one beam pair, for ambiguity resolution and to measurevelocity according to an embodiment of the disclosed technology,

FIG. 16 is a block diagram of a small aperture acoustic velocity sensor,according to an embodiment of the disclosed technology.

FIG. 17 is a flowchart of a process for measuring velocity according toan embodiment of the disclosed technology.

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

Acoustic velocity measurement instruments used in underwater vehicles,among other applications, can be configured with small aperture acousticvelocity sensor (SAAVS) transducer arrays having a number of phasedarray sub-arrays. Each transducer generates a beam of acoustic energy.Measurement of the three velocity components using acoustic phasedifferences in both time and space allows unusually good performanceeven when the aperture is small. This makes the acoustic beamsrelatively wide compared to existing high-performance Doppler velocitylogs of the same frequency. It also has advantages for high-speedapplications.

Embodiments of the disclosed technology overcome certain disadvantagesof correlation velocity logs. The SAAVS avoids specular return nearnadir by using spatial modulation to create multiple slanted acousticbeams. It also avoids having to model the bottom backscattercharacteristics with multiple parameters by using somewhat narrower andmore slanted acoustic beams. It also avoids the low signal to noiseratio (SNR) and high flow noise of cross-correlations of individualarray elements typically used in CVLs by forming a weighted average ofspatially-demodulated sub-array returns over nearly the entire availableaperture before the non-linear cross-correlation step. It also canimprove the SNR by using the entire available aperture for projection.Furthermore, it can overcome the discrete nature of thecross-correlation domain by using spatial and/or temporal interpolationbefore the cross-correlation step to make accurate estimates of thephase and amplitude at or near the point of peak cross-correlationmagnitude in time and space.

The disclosed technology includes a number of innovative features. Itcan use weighted interpolation of sub-array measurements to spatiallyshift the array centroid for projection and/or hydrophone receipt ofechoes and cross-correlation of successive pulses to improve correlationand reduce bias. The disclosed technology uses spatial modulation for aprojected signal. The disclosed technology measures spatial phase slopeacross the set of sub-arrays allowing correction of both long- andshort-term errors. The disclosed technology can use both spatial andtemporal interpolation. The disclosed technology makes efficient use ofthe available aperture. The disclosed technology can use phasemeasurements to measure two or three velocity components and tocalculate the spatial lags necessary to optimize performance.

One way of describing how the disclosed technology works is to considerthe pattern in a horizontal plane of an acoustic bottom echo from ahorizontally-moving continuous narrowband source. Due to incoherentbackscatter from a random collection of scatterers on a bottom that isrough compared to the acoustic wavelength, there is a random echopattern that will tend to move in the opposite direction from the sourcemotion with equal speed before eventually changing to a differentpattern. A cross-correlation of acoustic signal measurements that tracksthis pattern motion in time and space is a sensitive measure of movementbecause the variability in the pattern itself (known as “phase noise”when not tracked) is not included in the measurement. The same principleapplies to broadband signals that repeat at or near the time lag of thecross-correlation measurement. The description above describes theprinciple that allows all correlation velocity logs to work. The SAAVSapplies the same principle to a Doppler velocity log having multipleslanted acoustic beams.

FIG. 1 is a schematic diagram illustrating the first step in athree-step introduction to the theory of operation of the disclosedtechnology. Projectors TX1 and TX2, and hydrophones (receivers) RX1 andRX2 are spaced along the direction of travel. Forward projector TX1 andaft projector TX2 each project a short acoustic signal in the samedirection at times t_(TX1) and t_(TX2), respectively. Each signalfollows a path 125 towards a scattering object 130, and echoes off ofscattering object 130 along path 135 to be received by hydrophones RX1and RX2 at times t_(RX1) and t_(RX2), respectively. The time lag(t_(TX2)−t_(TX1)) is set equal to the ratio of vehicle speed toprojector spacing such that the two projectors are aligned in identicallocations relative to the bottom when projecting the same part of thesignal.

Hydrophones RX1 and RX2 have the same spacing as projectors TX1 and TX2,and receive the respective echoes off of a representative scatteringobject 130 along path 135 at identical locations and with the same timelag (t_(RX2)−t_(RX1)=t_(TX2)−t_(TX1)) as there was between the projectedsignals. When shifted by the time lag (t_(TX2)−t_(TX1)), the signalswill match no matter which direction the acoustic beam points becausethe sound takes identical paths. In general, the speed will not exactlymatch the ratio of transducer spacing to the time lag between theprojected signals, and the velocity vector will not be exactly alignedwith the vector of spatial displacement between transducers. The phaseof the demodulated correlation function is a sensitive measure of thevelocity component in the direction of the acoustic beam just like anordinary Doppler velocity log, but now with a velocity offset making thephase zero at the nominal velocity that makes both pulses followidentical paths.

FIG. 2 is a schematic diagram illustrating the second step in thethree-step introduction to the theory of operation of the disclosedtechnology. For the second step, we relax the condition that theprojector and hydrophone pairs TX1/TX2 and RX1/RX2, respectively, musthave identical spatial separations, replacing it with the more generalcondition that the sum of the projector and hydrophone separations onthe moving vehicle matches twice the product of the speed and the lagtime between projected pulses at the nominal offset velocity. Forexample, a single projector 210 can send two pulses at each of timest_(TX1) and t_(TX2) along paths 225 and 230 towards scattering object130 (and even more than two successive pulses at the same time lag) ifthe spacing of the hydrophone pair is doubled or the time lag is halvedrelative to those of the first step. These two pairs of pulses arereflected (echoed) off of scattering object 130 towards hydrophones RX1and RX2 along paths 235 and 240, where they are received at timest_(RX1) and t_(RX2), respectively.

The reason this still works is the bistatic invariance principle,described below with respect to FIG. 4, which stems from the fact thatthe relative phases among a group of scatterers will be the same for anytwo pairs of down-going ray paths 225 and 230, and up-going ray paths235 and 240 that share the same angle bisector even though thescattering angles differ. In the single-projector example, illustratedschematically in FIG. 2, the location of the second hydrophone RX2relative to the bottom is behind the location of the first hydrophoneRX1 one lag time earlier by the same distance that the projector hasmoved forward relative to the bottom in the lag time, keeping the anglebisectors the same for the ray paths of the two pulses. Benefits couldarise from stopping at this second step.

FIG. 3 is a schematic diagram illustrating the third step in thethree-step introduction to the theory of operation of the disclosedtechnology. A single projector 210 a can send two pulses at each oftimes t_(TX1) and t_(TX2) along paths 325 and 330 towards scatteringobject 130 if the time lag (t_(TX2)−t_(TX1)) between them is the same orshorter than that of the previous step. These two pulses are reflected(echoed) off of scattering object 130 towards hydrophones RX1 and RX2along paths 335 and 340, where they are received at times t_(RX1) andt_(RX2), respectively. For the third step, the practical difficulty ofcreating overlapping sub-arrays having a particular spatial displacementis overcome by interpolating measurements between non-overlapping phasedarray segments using a weighted average with different weights at eachreceive time. In an embodiment, the non-overlapping phased arraysegments (“sub-arrays”) are abutting or nearly so. Using interpolationto create this centroid shift allows continuous adjustment of spatiallag with only a small cost in reduced correlation magnitude.

The bistatic invariance principle is illustrated in FIG. 4. Suppose thatthe array is level and the vehicle is moving to the right with a smallupward component to the velocity. The four circles 401-404 along theline sloping gently upward at 10° represent from left to right thesuccessive positions, relative to the bottom 405, occupied by thephysical center of the array (which functions as both projector arrayand hydrophone array), 401 and 402 at the times of projection of twoseparate pings and 403 and 404 upon receipt of the two echoes separatedby approximately the same projection time lag T_(L). Using interpolationby weighted averaging of sub-arrays as illustrated in FIG. 3, theeffective centroid of the hydrophone array can be shifted horizontallyfrom the physical center as indicated by the dotted arrows (403→406 and404→407), effectively swapping the positions of the hydrophone arraycentroid at the two receive times and then shifting them a bit fartherapart to allow for the vertical component of velocity.

For convenience, with only a slight approximation we can simplify thepicture by projecting the velocity and hydrophone displacements onto theplane indicated by the line 408 that is perpendicular to the acousticbeam axis 409. The sound ray paths 410 and 411 to a scatterer on thebottom at the acoustic beam pattern centroid 412 and back form twoisosceles triangles, the angle bisectors of both the outer paths of thefirst pulse and the inner paths of the second pulse matching theacoustic beam axis 409. When this bistatic invariance geometry occurs,the angle χ between the down-going paths will match the similar anglebetween the up-going paths. This will be ensured if the spacing of theprojected projector locations matches the spacing of the projecteddisplaced hydrophone centroids.

Bistatic invariance geometry is sometimes referred to as phase centercoincidence, the term “phase center” meaning for each pulse the midpointbetween the projected positions of the effective centroids of theprojector and hydrophone relative to the bottom. In FIG. 4, the phasecenters coincide at the intersection of the acoustic beam axis 409 andits perpendicular 408. The outer (413 and 416) and inner (414 and 415)projected projector-hydrophone centroid pairs act as the foci of twoellipsoidal surfaces of constant travel time, represented by the twoelliptical arcs 418 and 419 drawn through the bottom scatterer on theacoustic beam axis 412, where they are tangent to each other. Becausethe ellipsoids are tangent, the difference in travel time is nearlyconstant for all scatterers in the neighborhood of the point oftangency, which should include most of the acoustic beam. Although thephase of each of these scatterers is random, their differences in phasefrom one pulse to the next will be nearly the same for all, resulting ina high correlation coefficient at the lag between pulse echo arrivals.When the bistatic invariance condition is not met, the ellipsoidsintersect, making the phase difference vary across the acoustic beam andreducing the correlation of the measurements.

Note that for clarity FIG. 4 is not drawn to scale. The meaneccentricity of the ellipsoids is actually on the order of the Machnumber and the angles χ between paths (in radians) are on the order ofthe product of the Mach number and the ratio of inter-pulse intervalT_(L) to travel time. Although FIG. 4 illustrates the bistaticinvariance principle in the context of bottom scattering, the principlealso applies analogously to a time-gated scattering volume that is partof a measured velocity profile or that is being used in a DVL to measurevehicle velocity when the bottom is not within range or to measurecurrent in anticipation of bottom track being lost in the future.

Now a quantitative theory of operation will be disclosed for the SAAVStechnology. For simplicity, an embodiment is described having fouracoustic beams numbered 1 to 4, all nominally at Janus angle J₀=30° tothe vertical, and having azimuth directions 90° apart aligned with theinterpolation axes. For this particular embodiment, the x axis isaligned laterally across the vehicle, positive to starboard, withacoustic beam 1 pointed to port and acoustic beam 2 to starboard. The yaxis is aligned longitudinally, positive forward, with acoustic beam 3pointed forward and acoustic beam 4 pointed aft. The z axis is nominallyupward when the vehicle is level. For this embodiment, the phased arraystave spacing is ½ wavelength at the center frequency of the projectedsignal and the phase change per stave is 90° for signals arriving at thenominal Janus angle. Those skilled in the art will understand that thistheory can easily be extended to other geometries, including otherinterpolation geometries, other array spacings, other array phasings,fewer acoustic beams or velocity components, or to an arrayconfiguration that uses switching, multiplexing, or a large number ofsimultaneous channels instead of or in addition to interpolation toshift the array centroid as needed to satisfy the bistatic invariancecondition, at least approximately.

The theory presented here is only a first-order approximation; varioussmall potential bias terms have been omitted for simplicity. Thoseskilled in the art will also understand that it can be desirable toinclude various undisclosed bias and other error corrections and that avariety of approaches to error correction are available, includingasymptotic expansion and empirical or semi-empirical calibration andthat algorithmic iteration can be required in some approaches. Thoseskilled in the art will also understand that the theory can be extendedto include the effects of pitch, roll, yaw, and their rates, as well aslinear acceleration, all of which have been neglected in this disclosurefor simplicity.

Consider position displacements in the bottom frame of reference due tolevel constant-velocity motion over the short lag interval T_(L) andhorizontal hydrophone array displacement d in the vehicle frame, asillustrated in FIGS. 3 and 4. Demodulated sample pairs are correlated ata time interval nominally equal to an integer multiple of the pulserepetition interval T_(L). Besides being displaced in time, the samplesof each pair also can be spatially displaced in the nominally-horizontalplane of the array to increase the correlation by satisfying thebistatic invariance condition, at least partially. We assume here thatthe displacement of the array centroid is being accomplished byinterpolation among sub-arrays, although other means could be usedinstead. The motions of both the vehicle relative to the bottom and thehydrophone array relative to the vehicle are detected by projecting themonto the four acoustic beams.

The phase (in radians) measured in the four acoustic beams shouldtheoretically obey the following equations:

$\begin{matrix}{\varphi_{1} = {{\frac{\pi}{U_{a}}\left( {{{- u}\mspace{14mu} \sin \mspace{14mu} J_{1}} - {w\mspace{20mu} \cos \mspace{14mu} J_{1}}} \right)} - {\frac{\pi}{2U_{a}T_{L}}d_{x\; 1}\mspace{14mu} \sin \mspace{14mu} J_{1}}}} & (1) \\{\varphi_{2} = {{\frac{\pi}{U_{a}}\left( {{u\mspace{14mu} \sin \mspace{14mu} J_{2}} - {w\mspace{20mu} \cos \mspace{14mu} J_{2}}} \right)} + {\frac{\pi}{2U_{a}T_{L}}d_{x\; 2}\mspace{14mu} \sin \mspace{14mu} J_{2}}}} & (2) \\{\varphi_{3} = {{\frac{\pi}{U_{a}}\left( {{v\mspace{14mu} \sin \mspace{14mu} J_{3}} - {w\mspace{20mu} \cos \mspace{14mu} J_{3}}} \right)} + {\frac{\pi}{2U_{a}T_{L}}d_{y\; 3}\mspace{14mu} \sin \mspace{14mu} J_{3}}}} & (3) \\{\varphi_{4} = {{\frac{\pi}{U_{a}}\left( {{{- v}\mspace{14mu} \sin \mspace{14mu} J_{4}} - {w\mspace{20mu} \cos \mspace{14mu} J_{4}}} \right)} - {\frac{\pi}{2U_{a}T_{L}}d_{y\; 4}\mspace{14mu} \sin \mspace{14mu} J_{4}}}} & (4)\end{matrix}$

The velocity components u, v, and w are those of the vehicle relative tothe bottom and U_(a) is the π-phase ambiguity velocity, making U_(a)T_(L)=¼ λ, where λ is the acoustic wavelength. In general, thehydrophone displacement can be different for each acoustic beam, so wehave distinguished the displacements by using the symbol d_(an) torepresent the hydrophone array displacement in the direction of axis afor acoustic beam n.

Eqns. 1-4 show that the phase of each acoustic beam measures thevelocity and displacement projected onto the acoustic beam axis. Incontrast, the bistatic invariance condition relates to the velocity anddisplacement projected onto the plane perpendicular to the acoustic beamaxis, at least to the order of approximation being considered here.Motion can be detected in this perpendicular plane by locating thecorrelation peak with variation in the hydrophone displacement byvarying the interpolation parameters to maximize the correlationmagnitude. This CVL method has more short-term and long-term error thanthe acoustic beam-axis Doppler phase measurement, but lacking the phaseambiguity of the latter method, it can be useful for ambiguityresolution. Even if the correlation peak is not searched for, operatingat or near the peak minimizes the standard deviation of the Dopplerphase measurement. Neglecting higher-order bias terms, bistaticinvariance imposes the following constraints, two for each acousticbeam:

2T _(L)(u cos J ₁ −w sin J ₁)+d _(x1) cos J ₁=0  (5)

2T _(L) v+d ₁=0  (6)

2T _(L)(u cos J ₂ +w sin J ₂)+d _(x2) cos J ₂=0  (7)

2T _(L) v+d _(y2)=0  (8)

2T _(L) u+d _(x3)=0  (9)

2T _(L)(v cos J ₃ +w sin J ₃)+d _(y3) cos J ₃=0  (10)

2T _(L) u+d _(x4)=0  (11)

2T _(L)(v cos J ₄ −w sin J ₄)+d _(y4) cos J ₄=0  (12)

It is convenient to define mean Janus angles J_(x)=½(J₁+J₂) andJ_(y)=½(J₃+J₄) and angle differences ΔJ_(x)=J₁−J₂ and ΔJ_(y)=J₃−J₄ forthe acoustic beam pairs. Typically, the Janus angle differences aresmall unknown noises that average to zero. It is also convenient tosimilarly define mean acoustic beam pair phases φ_(x)=½(φ₁+φ₂) andφ_(y)=½(φ₃+φ₄) and pair phase differences Δφ_(x)=φ₁−φ₂ and Δφ_(y)=φ₃−φ₄,along with mean pair hydrophone displacement componentsd_(x12)=½(d_(x1)+d_(x2)), d_(y12)=½(d_(y1)+d_(y2)),d_(x34)=½(d_(x3)+d_(x4)) and d_(y34)=½(d_(y3)+d_(y4)) and pairdisplacement difference components Δd_(x12)=d_(x1)−d_(x2),Δd_(y12)=d_(y1)−d_(y2), Δd_(x34)=d_(x3)−d_(x4) andΔd_(y34)=d_(y3)−d_(y4).

With these substitutions, phase equations Eqns. 1-4 become:

$\begin{matrix}{{\Delta\varphi}_{x} = {{- \frac{2\pi}{U_{a}}}\left( {{\left( {u + \frac{d_{x\; 12}}{2T_{L}}} \right)\sin \mspace{14mu} J_{x}\mspace{14mu} {\cos \left( {\frac{1}{2}\mspace{14mu} \Delta \mspace{20mu} J_{x}} \right)}} + {\left( {{{- w}\mspace{14mu} \tan \mspace{14mu} J_{x}} + \frac{\Delta \; d_{x\; 12}}{4T_{L}}} \right)\cos \mspace{14mu} J_{x}\mspace{14mu} {\sin \left( {\frac{1}{2}\mspace{14mu} \Delta \mspace{14mu} J_{x}} \right)}}} \right)}} & (13) \\{{\Delta\varphi}_{y} = {\frac{2\pi}{U_{a}}\left( {{\left( {v + \frac{d_{y\; 34}}{2T_{L}}} \right)\sin \mspace{14mu} J_{y}\mspace{14mu} {\cos \left( {\frac{1}{2}\mspace{14mu} \Delta \mspace{20mu} J_{y}} \right)}} + {\left( {{w\mspace{14mu} \tan \mspace{14mu} J_{y}} + \frac{\Delta \; d_{y\; 34}}{4T_{L}}} \right)\cos \mspace{14mu} J_{y}\mspace{14mu} {\sin \left( {\frac{1}{2}\mspace{14mu} \Delta \mspace{14mu} J_{y}} \right)}}} \right)}} & (14) \\{\varphi_{x} = {{- \frac{\pi}{U_{a}}}\left( {{\left( {u + \frac{d_{x\; 12}}{2T_{L}}} \right)\cos \mspace{14mu} J_{x}\mspace{14mu} {\sin \left( {\frac{1}{2}\mspace{14mu} \Delta \mspace{20mu} J_{x}} \right)}} + {\left( {{w\mspace{14mu} \cot \mspace{14mu} J_{x}} + \frac{\Delta \; d_{x\; 12}}{4T_{L}}} \right)\sin \mspace{14mu} J_{x}\mspace{14mu} {\cos \left( {\frac{1}{2}\mspace{14mu} \Delta \mspace{14mu} J_{x}} \right)}}} \right)}} & (15) \\{\varphi_{y} = {\frac{\pi}{U_{a}}\left( {{\left( {v + \frac{d_{y\; 34}}{2T_{L}}} \right)\cos \mspace{14mu} J_{y}\mspace{14mu} {\sin \left( {\frac{1}{2}\mspace{14mu} \Delta \mspace{20mu} J_{y}} \right)}} + {\left( {{{- w}\mspace{14mu} \cot \mspace{14mu} J_{y}} + \frac{\Delta \; d_{y\; 34}}{4T_{L}}} \right)\sin \mspace{14mu} J_{y}\mspace{14mu} {\cos \left( {\frac{1}{2}\mspace{14mu} \Delta \mspace{14mu} J_{y}} \right)}}} \right)}} & (16)\end{matrix}$

The bistatic invariance conditions Eqns. 5-12 become:

$\begin{matrix}{{d_{x\; 12} + {2T_{L}u} - {\frac{1}{2}\left( {{\Delta \; d_{x\; 12}} + {4T_{L}\mspace{14mu} w\mspace{14mu} \cot \mspace{14mu} J_{x}}} \right)\mspace{14mu} \tan \mspace{14mu} J_{x}\mspace{14mu} {\tan \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}}} = 0} & (17) \\{\mspace{76mu} {{d_{y\; 12} + {2T_{L}v}} = 0}} & (18) \\{\mspace{76mu} {{d_{x\; 34} + {2T_{L}u}} = 0}} & (19) \\{{d_{y\; 34} + {2T_{L}v} - {\frac{1}{2}\left( {{\Delta \; d_{y\; 34}} - {4T_{L}\mspace{14mu} w\mspace{14mu} \cot \mspace{14mu} J_{y}}} \right)\tan \mspace{14mu} J_{y}\mspace{14mu} {\tan \left( {\frac{1}{2}\Delta \mspace{14mu} J_{y}} \right)}}} = 0} & (20) \\{{{\Delta \; d_{x\; 12}} - {4T_{L}\mspace{14mu} w\mspace{14mu} \tan \mspace{14mu} J_{x}} - {2\left( {d_{x\; 12} + {2T_{L}u}} \right)\mspace{14mu} \tan \mspace{14mu} J_{x}\mspace{14mu} {\tan \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}}} = 0} & (21) \\{\mspace{76mu} {{\Delta \; d_{y\; 12}} = 0}} & (22) \\{\mspace{76mu} {{\Delta \; d_{x\; 34}} = 0}} & (23) \\{\mspace{76mu} {{{\Delta \; d_{y\; 34}} + {4T_{L}\mspace{14mu} w\mspace{14mu} \tan \mspace{14mu} J_{y}} - {2\left( {d_{y\; 34} + {2T_{L}v}} \right)\tan \mspace{14mu} \left( {\frac{1}{2}\Delta \mspace{14mu} J_{y}} \right)}} = 0}} & (24)\end{matrix}$

Suppose that the embodiment allows displacement in both horizontaldimensions, and that we choose the following hydrophone displacementvalues, which are approximate in the sense that they satisfy Eqns. 17,20, 21, and 24 only when the acoustic beam Janus angles match withineach pair (i.e. ΔJ=ΔJ_(y)=0):

d _(x12) =d _(x34)=2T _(L) u  (25)

d _(y12) =d _(y34)=−2T _(L) v  (26)

Δd _(x12)=4T _(L) w tan J _(x)  (27)

Δd _(y34)=−4T _(L) w tan J _(y)  (28)

Δd _(y12) =Δd _(x34)=0  (29)

Then with these hydrophone displacement values, Eqns. 13-16 become:

$\begin{matrix}{{\Delta\varphi}_{x} = {{\Delta\varphi}_{y} = 0}} & (30) \\{\varphi_{x} = {{{- \frac{\pi}{U_{a}}}w\frac{\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}{\cos \mspace{14mu} J_{x}}} \cong {{- \frac{\pi}{U_{a}}}w\mspace{14mu} \sec \mspace{14mu} J_{x}}}} & (31) \\{\varphi_{y} = {{{- \frac{\pi}{U_{a}}}w\frac{\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{y}} \right)}{\cos \mspace{14mu} J_{y}}} \cong {{- \frac{\pi}{U_{a}}}w\mspace{14mu} \sec \mspace{14mu} J_{y}}}} & (32)\end{matrix}$

Interestingly, Eqns. 25-28 null the phase differences (Eqns. 13 and 14)even when the acoustic beams have different Janus angles, no matter whatthose angles are. Furthermore, when the Janus angles do match in eachacoustic beam pair, the horizontal velocity components decouple from thevertical velocity and can therefore be detected without bias fromuncertainty in either Janus angle or sound speed by varying d_(x12) andd_(y34) until the phase nulls are found, so long as the gain factors sinJ_(x) and sin J_(y) are non-zero. In contrast, the vertical componentcan be measured through the mean phases φ_(x) and φ_(y), but these canbe biased by errors in Janus angle or sound speed.

In general, the maximum possible correlation may be reached for anyparticular acoustic beam at a displacement point other than that givenby Eqns. 25-29, for a number of reasons including Janus angledifferences within acoustic beam pairs. Some embodiments can seek toincrease the correlation by using different displacements than these, inwhich case Eqns. 13-16 can be inverted to solve for the velocitycomponents. The Janus angle of an acoustic beam can be estimated in anumber of ways, including using the slope of the acoustic beam phasewith respect to changes in the interpolation parameter.

For an embodiment having only one horizontal interpolation axis, say they axis aligned with acoustic beams 3 and 4, and three measured velocitycomponents, perhaps using an array similar to that shown in FIG. 6, itis not possible to select non-zero values for d_(x12), d_(x34), andΔd_(x34). In that case, Eqns. 25 and 27 would not apply. Instead ofEqns. 30-32, we would have:

$\begin{matrix}{{\Delta\varphi}_{x} = {{\frac{2\pi}{U_{a}}\left( {{{- u}\mspace{14mu} {\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}} + {w\mspace{14mu} {\sin \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}}} \right)\sin \mspace{14mu} J_{x}} \cong {{- \frac{\pi}{U_{a}}}u\mspace{14mu} \sin \mspace{14mu} J_{x}}}} & (33) \\{\mspace{76mu} {{\Delta\varphi}_{y} = 0}} & (34) \\{\varphi_{x} = {{{- \frac{\pi}{U_{a}}}\left( {{u\mspace{14mu} {\sin \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}} + {w\mspace{14mu} {\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}}} \right)\cos \mspace{14mu} J_{x}} \cong {{- \frac{\pi}{U_{a}}}w\mspace{14mu} \cos \mspace{14mu} J_{x}}}} & (35) \\{\mspace{76mu} {\varphi_{y} = {{{- \frac{\pi}{U_{a}}}w\frac{\cos \left( {\frac{1}{2}\Delta \mspace{20mu} J_{y}} \right)}{\cos \mspace{14mu} J_{y}}} \cong {{- \frac{\pi}{U_{a}}}w\mspace{14mu} \sec \mspace{14mu} J_{y}}}}} & (36)\end{matrix}$

Acoustic beams 1 and 2 would behave like those of an ordinary DopplerDVL, except that the correlation would be improved by the arraydisplacement along the y axis. Acoustic beams 3 and 4 would behave likethose of the two-interpolation-axes SAAVS embodiment described above,except that the correlation can be somewhat lower due to the lack ofarray displacement along the x axis. When the lateral velocity componentv is significant compared to u, there would be decorrelation in allacoustic beams and consequent increased standard deviation in allvelocity components compared to an embodiment having two interpolationaxes.

Because each sub-array of the phased array already performs spatialdemodulation in determining the phase of the arriving signal relative toa particular point on the array, it is convenient and natural to use aweighted combination of these phases when interpolating. Suppose we usethe centroid of each sub-array as its phase reference point. If thesub-array centroids are separated by an integer multiple of twowavelengths (four staves for this embodiment), then for a signalarriving from a single source at the nominal acoustic beam angle therewill be no apparent phase difference between the sub-arrays, even thoughthe phase difference is theoretically an integer multiple of 2π. Whenapplied to the phase change resulting from a particular hydrophonedisplacement that has been created by shifting the centroid of aweighted-average array synthesized with real weights, the effect ofspatial demodulation is to shift the phase in acoustic beam 3, say, by

$\frac{\pi}{2U_{a}T_{L}}{d_{e}\left( {{\sin \mspace{14mu} J_{3}} - {\sin \mspace{14mu} J_{0}}} \right)}$

instead of

$\frac{\pi}{2U_{a}T_{L}}d_{3}\mspace{14mu} \sin \mspace{14mu} {J_{3}.}$

The receive acoustic beam direction can be shifted slightly byintroducing a complex “twiddle factor” to the weights that combine thesub-arrays. In that case, J₀ in the expression means the adjusteddirection rather than 30°. We can modify Eqns. 1-4 to recognize thespatial demodulation effect on phase. Eqns. 13-16 respectively become:

$\begin{matrix}{{\Delta\varphi}_{x} = {{- \frac{2\pi}{U_{a}}}\left( {{\left( {u + \frac{d_{x\; 12}}{2T_{L}}} \right)\sin \mspace{14mu} J_{x}\mspace{14mu} {\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}} + {\left( {{{- w}\mspace{14mu} \tan \mspace{14mu} J_{x}} + \frac{\Delta \; d_{x\; 12}}{4T_{L}}} \right)\cos \mspace{14mu} J_{x}\mspace{14mu} {\sin \left( {\frac{1}{2}\Delta \mspace{11mu} J_{x}} \right)}} - {\frac{d_{x\; 12}}{2T_{L}}\sin \mspace{14mu} J_{0}}} \right)}} & (37) \\{{\Delta\varphi}_{y} = {\frac{2\pi}{U_{a}}\left( {{\left( {v + \frac{d_{y\; 34}}{2T_{L}}} \right)\sin \mspace{14mu} J_{y}\mspace{14mu} {\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{y}} \right)}} + {\left( {{w\mspace{14mu} \tan \mspace{14mu} J_{y}} + \frac{\Delta \; d_{y\; 34}}{4T_{L}}} \right)\cos \mspace{14mu} J_{y}\mspace{14mu} {\sin \left( {\frac{1}{2}\Delta \mspace{11mu} J_{y}} \right)}} - {\frac{d_{y\; 34}}{2T_{L}}\sin \mspace{14mu} J_{0}}} \right)}} & (38) \\{\varphi_{x} = {{- \frac{\pi}{U_{a}}}\left( {{\left( {u + \frac{d_{x\; 12}}{2T_{L}}} \right)\cos \mspace{14mu} J_{x}\mspace{14mu} {\sin \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}} + {\left( {{w\mspace{14mu} \cot \mspace{14mu} J_{x}} + \frac{\Delta \; d_{x\; 12}}{4T_{L}}} \right)\sin \mspace{14mu} J_{x}\mspace{14mu} {\cos \left( {\frac{1}{2}\Delta \mspace{11mu} J_{x}} \right)}} - {\frac{\Delta \; d_{x\; 12}}{4T_{L}}\sin \mspace{14mu} J_{0}}} \right)}} & (39) \\{\varphi_{y} = {\frac{\pi}{U_{a}}\left( {{\left( {v + \frac{d_{y\; 34}}{2T_{L}}} \right)\cos \mspace{14mu} J_{y}\mspace{14mu} {\sin \left( {\frac{1}{2}\Delta \mspace{14mu} J_{y}} \right)}} + {\left( {{{- w}\mspace{14mu} \cot \mspace{14mu} J_{y}} + \frac{\Delta \; d_{y\; 34}}{4T_{L}}} \right)\sin \mspace{14mu} J_{y}\mspace{14mu} {\cos \left( {\frac{1}{2}\Delta \mspace{11mu} J_{y}} \right)}} - {\frac{\Delta \; d_{y\; 34}}{4T_{L}}\sin \mspace{14mu} J_{0}}} \right)}} & (40)\end{matrix}$

Using the hydrophone displacements from Eqns. 25-29 exactly as before,Eqns. 30-32 become:

$\begin{matrix}{\mspace{76mu} {{\Delta\varphi}_{x} = {{- \frac{2\pi}{U_{a}}}u\mspace{14mu} \sin \mspace{14mu} J_{0}}}} & (41) \\{\mspace{76mu} {{\Delta\varphi}_{y} = {\frac{2\pi}{U_{a}}v\mspace{14mu} \sin \mspace{14mu} J_{0}}}} & (42) \\{\varphi_{x} = {{{- \frac{\pi}{U_{a}}}w\frac{{\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)} - {\sin \mspace{14mu} J_{x}\mspace{14mu} \sin \mspace{14mu} J_{0}}}{\cos \mspace{14mu} J_{x}}} \cong {{- \frac{\pi}{U_{a}}}{w\left( {{\sec \mspace{14mu} J_{x}} - {\tan \mspace{14mu} J_{x}\mspace{14mu} \sin \mspace{14mu} J_{0}}} \right)}}}} & (43) \\{\varphi_{y} = {{{- \frac{\pi}{U_{a}}}w\frac{{\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{y}} \right)} - {\sin \mspace{14mu} J_{y}\mspace{14mu} \sin \mspace{14mu} J_{0}}}{\cos \mspace{14mu} J_{y}}} \cong {{- \frac{\pi}{U_{a}}}{w\left( {{\sec \mspace{14mu} J_{y}} - {\tan \mspace{14mu} J_{y}\mspace{14mu} \sin \mspace{14mu} J_{0}}} \right)}}}} & (44)\end{matrix}$

Eqns. 41 and 42 show that the effect of spatial demodulation on thehorizontal velocity component is to make the SAAVS act like an idealDoppler DVL with the nominal Janus angle, corrected for bothterrain/absorption bias and stochastic deviations of the arrival angle.When ΔJ_(x)=ΔJ_(y)=0 and J_(x)=J_(y)=J₀, the trigonometric factor in thefinal expression of Eqns. 43 and 44 becomes cos J₀, as one would expectfrom an ideal Doppler DVL.

For the embodiment having only one interpolation axis, with spatialdemodulation Eqns. 33-36 become:

$\begin{matrix}{{\Delta\varphi}_{x} = {{\frac{2\pi}{U_{a}}\left( {{{- u}\mspace{14mu} {\cos \left( {\frac{1}{2}\Delta \mspace{20mu} J_{x}} \right)}} + {w\mspace{14mu} {\sin \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}}} \right)\sin \mspace{14mu} J_{x}} \cong {{- \frac{\pi}{U_{a}}}u\mspace{14mu} \sin \mspace{14mu} J_{x}}}} & (45) \\{\mspace{76mu} {{\Delta\varphi}_{y} = {\frac{2\pi}{U_{a}}v\mspace{14mu} \sin \mspace{14mu} J_{0}}}} & (46) \\{\varphi_{x} = {{{- \frac{\pi}{U_{a}}}\left( {{u\mspace{14mu} {\sin \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}} + {w\mspace{14mu} {\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{x}} \right)}}} \right)\cos \mspace{14mu} J_{x}} \cong {{- \frac{\pi}{U_{a}}}w\mspace{14mu} \cos \mspace{14mu} J_{x}}}} & (47) \\{\varphi_{y} = {{{- \frac{\pi}{U_{a}}}w\frac{{\cos \left( {\frac{1}{2}\Delta \mspace{14mu} J_{y}} \right)} - {\sin \mspace{14mu} J_{y}\mspace{14mu} \sin \mspace{14mu} J_{0}}}{\cos \mspace{14mu} J_{y}}} \cong {{- \frac{\pi}{U_{a}}}{w\left( {{\sec \mspace{14mu} J_{y}} - {\tan \mspace{14mu} J_{y}\mspace{14mu} \sin \mspace{14mu} J_{0}}} \right)}}}} & (48)\end{matrix}$

In this case, only the measurement of forward velocity v is unbiased(Eqn. 46). However, if terrain and absorption bias can be assumed to beindependent of acoustic beam azimuth, then the measured value of J_(y),perhaps after low-pass filtering, can be used to estimate J_(x).

For broad-bandwidth embodiments when there is no nominally-verticalvelocity component w (orthogonal to the array face), the side-peaks ofthe correlation function in time will have local maxima of correlationmagnitude at multiples of the pulse repletion interval T_(L) of theprojected signal, independent of horizontal velocity. However, the peaklocations can be Doppler-shifted by the w component of velocity, and thephase measurement at time lag T_(L) or an integer multiple of it can bebiased. A time-interpolation method to correct this bias is disclosed inU.S. Pat. No. 7,542,374. Interpolation in time adds another dimension tothe spatial interpolation described above.

Phase measurements from phased arrays are subject to bias due tosidelobe coupling between acoustic beams. Phased arrays with wideacoustic beams are particularly vulnerable to this problem because thesidelobes of their acoustic beam patterns tend to be higher than thoseof narrower acoustic beams. There are a number of ways to mitigate thisproblem, including using fewer acoustic beams at the same time,selecting acoustic beam patterns having a wide null in the direction ofany acoustic beams being used simultaneously, and a method usingdifferent codes on different acoustic beams disclosed in U.S. Pat. No.7,839,720.

FIG. 5 is a diagram of a grid 500 of four rectangular receive sub-arrays510 a, 510 b, 510 and 510 d that cover the full aperture of the transmitarray of a small aperture acoustic velocity sensor according to anembodiment of the disclosed technology. Each subarray includes aplurality of elements 505 arranged in rows and columns. A small apertureacoustic velocity sensor can perform interpolation along one axis, twoaxes, or a plurality of axes, depending upon the desired application. Aparticular embodiment of the small aperture acoustic velocity sensor,where interpolation is performed along two axes, is able to utilize thefull benefits resulting from interpolation and can estimate threeorthogonal velocity components.

FIG. 6 is a diagram of a grid 600 of two receive sub-arrays 510 a and510 b that cover the full aperture of the transmit array of a smallaperture acoustic velocity sensor according to an embodiment of thedisclosed technology. This embodiment of the small aperture acousticsensor, where interpolation is performed along one axis, is able toutilize the benefits resulting from interpolation and can also estimatethree orthogonal velocity components. When there is a lateral driftcomponent to the velocity, the correlation in all acoustic beams will beless than it could be if interpolation were available in the lateraldirection, although the correlation of all acoustic beams will beimproved compared to having no interpolation at all, reducing thestandard deviation of all velocity components. Also, biases attributableto non-ideal arrival angle will not be automatically corrected in thelateral direction, although an appropriate correction factor can bemeasured in the longitudinal direction and applied explicitly to thelateral velocity measurement. This should be effective so long as thebias is non-directional.

FIG. 7 is a diagram of a grid 700 of four identical hydrophonesub-arrays 710 a, 710 b, 710 c and 710 d having approximately hexagonalapertures, aligned with the two center sub-arrays abutting, that coverthe full aperture of the transmit array of a small aperture acousticvelocity sensor according to an embodiment of the disclosed technology.The array of FIG. 7 is similar to the array in FIG. 5 and can be used ina small aperture acoustic velocity sensor. A difference between thearray of FIG. 7 and FIG. 5 is the shape and layout of the sub-arrays. Anapproximately hexagonal shaped has a different acoustic beam patternthan a rectangular array and the response attenuation in certain spatialdirection can be improved compared to a rectangular array. It isdesirable for the acoustic beam pattern of an array to have a spatialresponse that is as low as possible in undesired directions to be ableto separate the angle of arrival of acoustic energy. There are typicallytradeoffs between acoustic beam pattern responses in differentdirections, where one array can have a lower response than another arrayin a given undesired direction, but a higher response in some otherundesired direction. Depending on the application, configuration,layout, and requirements, one particular array shape and thecorresponding acoustic beam pattern can be favored over other arrayshapes.

FIG. 8 is a diagram of a grid 800 of four identical receive sub-arrays710 a, 710 b, 710 c and 710 d having approximately hexagonal apertures,rotated by an amount to fit a rectangular surface, that cover the fullaperture of the transmit array of a small aperture acoustic velocitysensor according to an embodiment of the disclosed technology. The arrayof FIG. 8 is similar to the array in FIG. 7 and can be used in a smallaperture acoustic velocity sensor. A difference between the array ofFIG. 8 and FIG. 7 is the rotation and layout of the sub-arrays. Theparticular layout of the array in FIG. 8 is advantageous for fitting thefour sub-arrays in an approximately square surface of small area.

FIG. 9 is a diagram of a grid 900 of four identical receive sub-arrays710 a, 710 b, 710 c and 710 d having approximately hexagonal apertures,aligned such that there is a hole in the center, that cover the fullaperture of the transmit array of a small aperture acoustic velocitysensor according to an embodiment of the disclosed technology. The arrayof FIG. 9 is similar to the array in FIG. 8 and can be used in a smallaperture acoustic velocity sensor. A difference between the array ofFIG. 9 and FIG. 8 is the layout and the hole in the center of thesub-arrays. This layout can be beneficial in that the velocityprocessing algorithm could be simplified because the sub-arrays areoriented along perpendicular axes.

FIG. 10 is a diagram of a grid 1000 of four receive sub-arrays 1010 a,1010 b, 1010 c and 1010 d having approximately quarter-circle-shapedapertures that cover the full circular aperture of the transmit array ofa small aperture acoustic velocity sensor according to an embodiment ofthe disclosed technology. The array of FIG. 10 is similar to the arrayin FIG. 5 and can be used in a small aperture acoustic velocity sensor.A difference between the array of FIG. 10 and FIG. 5 is thequarter-circle shape of the sub-arrays. This particular shape isbeneficial for fitting the four sub-arrays in a circular surface of thesmallest possible area, but has the disadvantage that the sub-arrays areasymmetric and do not have identical orientations.

FIG. 11 is a diagram of a grid 1100 of four rectangular receivesub-arrays 1110 a, 1110 b, 1110 c and 1110 d, composed of elements 505that are rotated by an amount, that cover the full aperture of thetransmit array of a small aperture acoustic velocity sensor according toan embodiment of the disclosed technology. The array of FIG. 11 issimilar to the array in FIG. 5 and can be used in a small apertureacoustic velocity sensor. A difference between the array of FIG. 11 andFIG. 5 is the rotation of the grid elements in the array of FIG. 11along with the staves that connect elements having the same phase.Receive and transmit phasing is performed diagonally to form acousticbeams that are spatially oriented at an angle in azimuth from theoutline of the sub-arrays. Diagonal acoustic beam forming has theadvantage of tapering the aperture along the direction of the acousticbeam, leading to particularly low acoustic beam pattern response in theundesired direction of the opposite acoustic beam.

The arrays disclosed in FIG. 5 to FIG. 11 are composed of differentnumber of sub-arrays, shapes, layouts, and elements of differentrotations. There are many other possible array geometries that could becombinations of the disclosed arrays, alterations to the disclosedarrays, or other geometries that could be used in a small apertureacoustic velocity sensor. Certain advantages of the disclosed arrayswere identified, but it is not possible to disclose every possible arrayvariation and the corresponding advantage.

FIG. 12 illustrates a perspective view of a small aperture acousticvelocity sensor 1200 according to certain embodiments. The smallaperture acoustic velocity sensor 1200 consists of a pressure housing1240 with mounting holes 1250 on the side away from the acoustic array1210, an electrical connector, the array with four square sub-arrays1230 a, 1230 b, 1230 c and 1230 d, and contains the electronics insideof the pressure housing 1240. The arrays of this embodiment can be ofany shape, size, configuration, orientation, and can contain any numberof sub-arrays of elements 1220 of any shape, size, configuration, andorientation, such as the arrays illustrated in FIGS. 5-11.

FIG. 13 is a block diagram of an exemplary embodiment of the electronics1300 for a small aperture acoustic velocity sensor. There arealternative ways of configuring and partitioning the electronics of thesmall aperture acoustic velocity sensor that could achieve similarresults. When pinging all acoustic beams simultaneously a total of 16channels are required for dual axis interpolation, while 8 channels aresufficient for single-axis interpolation. Multiplexing of acoustic beamsand/or arrays is possible to reduce the required number of electronicschannels.

The implementation of the small aperture acoustic velocity sensor 1300is divided up into two domains: an analog domain 1305 and a digitaldomain 1310. Each of the four sub-arrays 1315 is composed of rows andcolumns of piezoelectric transmit and receive elements, similar to aconventional Doppler velocity log. There are four pairs of wires foreach array 1315 and they are connected to four of the channels 1320. Atransmit receive (T/R) switch 1325 multiplexes between transmit andreceive. In transmit mode a transmit waveform generator generates phasecoded waveforms for each of the sub arrays 1315 and the output isamplified by a power amplifier 1355.

In receive mode the output of the T/R switch 1325 is connected to ananalog front end block 1330 that can contain amplification stages,filters, and other analog components. In this embodiment, the output ofthe analog front end 1325 is digitized by an ADC 1335. Beamforming isperformed in the digital domain by beam former 1340, where at least twochannels are delayed in phase by different amounts and summed together.In-phase and quadrature (IQ) demodulation is performed by an IQdemodulator block 1345 and the signal is down-converted to baseband bymultiplication by a complex exponential. The last stage of each channelcontains a filter 1350 to filter out the unwanted parts of the frequencyspectrum after demodulation. The outputs of the 16 channels areconnected to a Doppler processor 1360, which processes the IQ dataaccording to a process to, for example, compute velocity. Dopplerprocessor 1360 can be a processor, an FPGA, or other computingcircuitry. One version of the process that can be implemented in theDoppler processing block is provided in the flow chart described below.

An I/O interface 1365 connects the system to a host and passesconfiguration data to a configuration module. The I/O interface 1365 isbi-directional and outputs the Doppler results to the host processor(not shown), and performs configuration writes and reads to and from theconfiguration module 1370. A power supply 1380 powers the system and isshown in FIG. 13.

FIG. 14 is a flowchart of a process 1400 for measuring velocityaccording to an embodiment of the disclosed technology for the dual axisof interpolation embodiment that is composed of two or four sub-arrays.Each of the steps of the method 1400 can be performed by Dopplerprocessor 1360, as illustrated in FIG. 13. For each acoustic beam thesub-arrays are used to interpolate to or near to the location of highestcorrelation. The interpolation will be described along only one axis forease of understanding using two sub-arrays, but the method can beextended to incorporate, for example, four sub-arrays as well asinterpolation in time.

In the description of the four sub-array DVL embodiment we assume thatprojection is set up in a manner similar to a conventional Dopplervelocity log, where a transmitted pulse is composed of a multitude ofsequences repeated at a time interval T_(L). Each of the four sub-arraysthen form Janus beams out of the plane of the arrays at an angle J fromthe axis perpendicular to the array. In the description of theinterpolation along one axis the two sub-arrays will be referred to assub-arrays A and B, the aft sub-array being A and the forward one towardthe bow being B.

Step 1.

At block 1410, the method 1400 locates the bottom for each acoustic beamand selects the data segments to be used. Using signal intensity orother means, the method 1400 determines suitable data segments to beused for cross-correlation. For these segments, the echo should bedominated by the echo from the bottom, without transients that wouldcause differences in the population of scatterers over the time intervalT_(L). In other embodiments that use water volume scattering,time-gating and data segment selection would be used instead to placeone or more depth cells at particular desired ranges.

Step 2.

At block 1420, the method 1400 computes the auto- and cross-correlationsamong sub-arrays at zero time lag and at least one other lag at or nearwhich the signal repeats. For each acoustic beam separately, the method1400 computes complex correlations among sub-arrays necessary toconstruct the magnitude and phase of the correlation coefficient as afunction of interpolation parameters. Let s_(Am) and s_(Bm) be them^(th) complex phasor samples representing the demodulated signalmeasurements from a particular acoustic beam in the A and B sub-arraysand δ_(yn) be the acoustic beam-n interpolation weight parameter used tocombine them to form the complex sample s_(i)(y_(v), t) by spatialinterpolation along the y axis. It is often useful to combine the twomeasurements with a relative phase offset α, particularly if thedistance D separating the centroids of sub-arrays A and B projected ontothe interpolation axis is not an integer multiple of 2λ, or if slightsteering of the acoustic beam centroid direction by a fraction of thebeamwidth is desired. If we choose the interpolation parameter δ_(yn) tohave the value 0 at the center position where both sub-arrays areweighted equally, −1 when the sample from sub-array A is selected, and 1when B is selected, the linear interpolation formula must be equivalentto:

$\begin{matrix}{{s_{i}\left( {{y_{v} = {\frac{1}{2}\delta_{yn}\mspace{14mu} D}},{t = {m\mspace{14mu} t}},_{s}} \right)} = {{\frac{1}{2}\left( {1 - \delta_{yn}} \right)^{\frac{1}{2}i\; \alpha}s_{A,m}} + {\frac{1}{2}\left( {1 + \delta_{yn}} \right)^{{- \frac{1}{2}}i\; \alpha}s_{B,m}}}} & (49)\end{matrix}$

y_(v) is the interpolated centroid position along the forward axis inthe vehicle frame relative to the physical centroid of the array, t istime and t_(s) is the sample interval. Since the centroid follows thesame linear weighting rule as the samples (assuming sub-arrays A and Bmatch), by substituting the sub-array positions ±½ D into Eqn. 49 forthe samples s_(Bn) and s_(An), respectively, we can see that thecentroid position of the combined array is y_(v)=½ δ_(yn) D. Althoughsymmetry is not strictly necessary, the preferred embodiment usesinterpolation parameters of equal magnitude and opposite signs whencross-correlating sample pairs at spatial lag d_(y)=δ_(yn) D.

$\begin{matrix}\begin{matrix}{{4{s_{i}\left( {y_{v},t} \right)}{s_{i}^{*}\left( {{y_{v} + {\delta_{n}\mspace{14mu} D}},{t + T_{L}}} \right)}} = \left( {{\left( {1 + \delta_{yn}} \right)^{\frac{1}{2}i\; \alpha}s_{A,m}} +} \right.} \\\left. {\left( {1 - \delta_{yn}} \right)^{{- \frac{1}{2}}i\; \alpha}s_{B,m}} \right) \\{\left( {{\left( {1 - \delta_{yn}} \right)^{{- \frac{1}{2}}i\; \alpha}s_{A,{({m + L})}}^{*}} +} \right.} \\\left. {\left( {1 - \delta_{yn}} \right)^{\frac{1}{2}i\; \alpha}s_{B,{({m + L})}}^{*}} \right) \\{= {{\left( {1 + \delta_{yn}} \right)^{2}^{i\; \alpha}s_{A,m}s_{B,{({m + L})}}^{*}} + \left( {1 - \delta_{yn}^{*}} \right)}} \\{{\left( {{s_{A,n}s_{A,{({m + L})}}^{*}} + {s_{B,n}s_{B,{({m + L})}}^{*}}} \right) +}} \\{{\left( {1 - \delta_{yn}} \right)^{2}^{{- i}\; \alpha}s_{B,m}s_{B,{({m + L})}}^{*}}}\end{matrix} & (50)\end{matrix}$

L is the lag in samples, making T_(L)=L t_(s) and the asterisk means thecomplex conjugate. By accumulating the three cross-correlation terms inEqn. 50 separately, the interpolation parameter δ_(yn) can be left as afree variable to be determined later in the velocity processingalgorithm. The phase and correlation coefficient of the interpolatedarray are then related to the cross-correlations among sub-arrays by:

$\begin{matrix}{{\varphi \left( {{\delta_{yn}D},T_{L}} \right)} = {\arg \left( {{\left( {1 + \delta_{yn}} \right)^{2}^{i\; \alpha}R_{{AB},L}} + {\left( {1 - \delta_{yn}^{2}} \right)\left( {R_{{AA},L} + R_{{BB},L}} \right)} + {\left( {1 - \delta_{yn}} \right)^{2}^{{- i}\; \alpha}R_{{BA},L}}} \right)}} & (51) \\{{\rho \left( {{\delta_{yn}D},T_{L}} \right)} = \frac{\begin{matrix}\left| {{\left( {1 + \delta_{yn}} \right)^{2}^{i\; \alpha}R_{{AB},L}} + {\left( {1 - \delta_{yn}^{2}} \right)\left( {R_{{AA},L} + R_{{BB},L}} \right)} +} \right. \\\left. {\left( {1 - \delta_{yn}} \right)^{2}^{{- i}\; \alpha}R_{{BA},L}} \right|\end{matrix}}{\sqrt{\begin{matrix}{\left( {{\left( {1 + \delta_{yn}^{2}} \right)\left( {R_{{AA},0} + R_{{BB},0}} \right)} + {\left( {1 - \delta_{yn}^{2}} \right)\left( {{^{i\; \alpha}R_{{AB},0}} + {^{{- i}\; \alpha}R_{{BA},0}}} \right)}} \right)^{2} -} \\{4{\delta_{yn}^{2}\left( {R_{{AA},0} - R_{{BB},0}} \right)}^{2}}\end{matrix}}}} & (52)\end{matrix}$

The Rs are the various accumulated correlation pairs shown in Eqn. 50 atsample lags L and 0. In Eqn. 52, the correlation coefficient has beennormalized by the geometric mean of the autocorrelations at zero timelag of the interpolated arrays having interpolation parameters δ_(yn)and −δ_(yn). Eqns. 51 and 52 are not actually executed until Step 4.

Step 3.

At block 1430, the method 1400 estimates velocity to resolve phaseambiguity. The method 1430 finds an approximation for the velocityvector that is close enough to prevent ambiguity errors in the nextstep. There are many possible approaches to estimate the velocity apriori or from the data of the present ping or using some combination ofpresent and past measurements. These include assuming that the velocityis zero, using the value from the previous measurement or a weightedaverage of previous measurements, using inertial sensors to estimate thechange in velocity from the previous measurement, using a filteredpressure sensor signal to estimate the vertical velocity component, andusing the disclosed algorithm for a shorter lag. If the initial velocityestimate is so unreliable that there is a significant chance ofambiguity error in the next step, then it is advisable to use an aposteriori method of ambiguity error detection, such as screening forlarge errors in the redundant velocity component when combining fouracoustic beam-axis components into three orthogonal velocity components;or varying the lag from ping to ping; or using two or more differentlags with data from the same ping. The method of ambiguity resolutiondisclosed here involves maximizing the correlation coefficient in eachof the planes perpendicular to an acoustic beam, by finding for eachacoustic beam the value of the interpolation parameter δ_(n) thatmaximizes the correlation coefficient of Eqn. 52. A number of searchalgorithms are available for such maximization problems. For theone-dimensional interpolation described here, the velocity estimatesare:

$\begin{matrix}{v \cong {{- \frac{D}{8T_{L}}}\left( {\delta_{y\; 1} + \delta_{y\; 2} + \delta_{y\; 3} + \delta_{y\; 4}} \right)}} & (53) \\{w \cong {\frac{D}{4T_{L}}\left( {\delta_{y\; 4} - \delta_{y\; 3}} \right)\cot \mspace{14mu} J_{y}}} & (54)\end{matrix}$

Stochastic variation in the curvature of the correlation coefficientwith the interpolation parameter near the peak occasionally makes thequality of the estimate from any one acoustic beam somewhat erratic, butbecause the acoustic beams are largely independent, the average given byEqn. 53, or a weighted version of it, should be useful as a startingpoint for v in the next step. The estimate for the vertical velocitycomponent w given in Eqn. 54 by the difference between the peakinterpolation parameters for two acoustic beams may be erratic somewhatmore often than the v estimate. Depending upon the circumstances,averaging and screening with other methods of ambiguity resolution maybe useful for ensuring a reliable starting value for all velocitycomponents.

Step 4.

At block 1440, the method 1400 computes the velocity vector andcorrelation coefficient at or near the optimal interpolation point. Themethod 1400 computes the velocity vector at a displacement pointconsistent with the velocity. A few iterations may be needed to ensureconsistency. The displacement point is initially computed assuming thevelocity vector determined in the previous step and using a version ofEqns. 25-29:

$\begin{matrix}{\delta_{x\; 1} = {{- 2}\frac{T_{L}}{D}\left( {u - {w\mspace{14mu} \tan \mspace{14mu} J_{x}}} \right)}} & (55) \\{\delta_{x\; 2} = {{- 2}\frac{T_{L}}{D}\left( {u + {w\mspace{14mu} \tan \mspace{14mu} J_{x}}} \right)}} & (56) \\{\delta_{x\; 3} = {\delta_{x\; 4} = {{- 2}\frac{T_{L}}{D}u}}} & (57) \\{\delta_{y\; 1} = {\delta_{y\; 2} = {{- 2}\frac{T_{L}}{D}v}}} & (58) \\{\delta_{y\; 3} = {{- 2}\frac{T_{L}}{D}\left( {v + {w\mspace{14mu} \tan \mspace{14mu} J_{y}}} \right)}} & (59) \\{\delta_{y\; 4} = {{- 2}\frac{T_{L}}{D}\left( {v - {w\mspace{14mu} \tan \mspace{14mu} J_{y}}} \right)}} & (60)\end{matrix}$

(For the embodiment using one-dimensional interpolation consideredabove, only Eqns. 58-60 would be used.) Using the interpolationparameters for each acoustic beam, the acoustic beam phases can becalculated using Eqn. 51 or its two-dimensional equivalent. The velocitycomponents can then be calculated from the acoustic beam phases. For theembodiment using one-dimensional interpolation, we can use anambiguity-resolving inversion of Eqns. 45-48, such as:

$\begin{matrix}{\mspace{76mu} \left. u\leftarrow{\frac{U_{a}}{\sin \mspace{14mu} J_{x}}\left( {\frac{\varphi_{2} - \varphi_{1}}{2\pi} + {{round}\left( {{\frac{\sin \mspace{14mu} J_{x}}{U_{a}}u} - \frac{\varphi_{2} - \varphi_{1}}{2\pi}} \right)}} \right)} \right.} & (61) \\{\mspace{76mu} \left. v\leftarrow{\frac{U_{a}}{\sin \mspace{14mu} J_{0}}\left( {\frac{\varphi_{3} - \varphi_{4}}{2\pi} + {{round}\left( {{\frac{\sin \mspace{14mu} J_{0}}{U_{a}}v} - \frac{\varphi_{3} - \varphi_{4}}{2\pi}} \right)}} \right)} \right.} & (62) \\\left. w\leftarrow{\frac{U_{a}}{{\cos \mspace{14mu} J_{x}} + {\sec \mspace{14mu} J_{y}} - {\tan \mspace{14mu} J_{y}\mspace{14mu} \sin \mspace{14mu} J_{0}}} \times \left( {{- \frac{\varphi_{1} + \varphi_{2} + \varphi_{3} + \varphi_{4}}{2\pi}} + {{round}\left. \quad\left( {{\frac{{\cos \mspace{14mu} J_{x}} + {\sec \mspace{14mu} J_{y}} - {\tan \mspace{14mu} J_{y}\mspace{14mu} \sin \mspace{14mu} J_{0}}}{U_{a}}w} + \frac{\varphi_{1} + \varphi_{2} + \varphi_{3} + \varphi_{4}}{2\pi}} \right) \right)}} \right.} \right. & (63)\end{matrix}$

U_(a)=¼ λ/T_(L) is the π-phase radial ambiguity velocity, the roundfunction finds the nearest integer to its argument, and the leftwardarrow symbol indicates assignment of the right-hand side value to thevariable on the left-hand side, updating that variable after it is usedin the expression on the right-hand side. Other weightings are possiblefor w besides that given by Eqn. 63. For the embodiment usingtwo-dimensional interpolation, on the other hand, we can use aninversion of Eqns. 41-44, such as:

$\begin{matrix}{\mspace{76mu} \left. u\leftarrow{\frac{U_{a}}{\sin \mspace{14mu} J_{0}}\left( {\frac{\varphi_{2} - \varphi_{1}}{2\pi} + {{round}\left( {{\frac{\sin \mspace{14mu} J_{0}}{U_{a}}u} - \frac{\varphi_{2} - \varphi_{1}}{2\pi}} \right)}} \right)} \right.} & (64) \\{\mspace{76mu} \left. v\leftarrow{\frac{U_{a}}{\sin \mspace{14mu} J_{0}}\left( {\frac{\varphi_{3} - \varphi_{4}}{2\pi} + {{round}\left( {{\frac{\sin \mspace{14mu} J_{0}}{U_{a}}v} - \frac{\varphi_{3} - \varphi_{4}}{2\pi}} \right)}} \right)} \right.} & (65) \\\left. w\leftarrow{\frac{U_{a}}{{\sec \mspace{14mu} J_{x}} + {\sec \mspace{14mu} J_{y}} - {\left( {{\tan \mspace{14mu} J_{x}} + {\tan \mspace{14mu} J_{y}}} \right)\sin \mspace{14mu} J_{0}}} \times \left( {{- \frac{\varphi_{1} + \varphi_{2} + \varphi_{3} + \varphi_{4}}{2\pi}} + {{round}\left. \quad\left( {{\frac{{\sec \mspace{14mu} J_{x}} + {\sec \mspace{14mu} J_{y}} - {\left( {{\tan \mspace{14mu} J_{x}} + {\tan \mspace{14mu} J_{y}}} \right)n\mspace{14mu} J_{0}}}{U_{a}}w} + \frac{\varphi_{1} + \varphi_{2} + \varphi_{3} + \varphi_{4}}{2\pi}} \right) \right)}} \right.} \right. & (66)\end{matrix}$

Other weightings are possible for w besides that given by Eqn. 66. TheStep 4 sequence of operations can be iterated until the velocitycomponents stop changing. There are several methods available to speedup convergence, but convergence is rapid simply with iteration alone.The final correlation coefficient for each acoustic beam can be computedafter convergence using Eqn. 52 or its two-dimensional equivalent.

FIG. 15 is a flowchart of a process for the last two steps of FIG. 14 inmore detail for the particular case of a single interpolation dimensionaligned with one beam pair, for ambiguity resolution and to measurevelocity according to an embodiment of the disclosed technology. In thedescription of four sub-array embodiments, as illustrated in FIG. 5, 7,8, 9, 11 or 12, we can assume that transmit is set up in a mannersimilar to a conventional Doppler velocity log, where a transmit pulseis composed of a multitude of repeated sequences separated by a time lagT_(L). Each of the four sub-arrays then form Janus beams out of theplane of the arrays at an angle J from the axis perpendicular to thearray. In the description of the interpolation along one axis the twosub-arrays will be referred to as the left and right sub-arrays. Each ofthe steps of the method 1500 can be performed by Doppler processor 1360,as illustrated in FIG. 13.

At block 1505, the method 1500 estimates velocity to resolve phaseambiguity, corresponding to block 1430 of the method 1400, as describedabove with respect to FIG. 14, for an embodiment having a singleinterpolation axis. Block 1505 includes blocks 1515, 1520, 1525, 1530and 1535, as described below. At block 1510, the method 1500 computesthe velocity and correlation coefficient at or near an optimalinterpolation point, corresponding to block 1440 of the method 1400, asdescribed above with respect to FIG. 14, for an embodiment having asingle interpolation axis. Block 1510 includes blocks 1540, 1545, and1550, as described below.

At block 1515, the method 1500 computes that correlation coefficientusing Eqn. 52 and finds the approximate location of the peak of thecorrelation coefficient with respect to variation of the interpolationparameter δ_(yn) for each acoustic beam, by finding the largest of a setof values calculated over a set of discrete values. The peak locationsare assigned to the variables δ_(y1,p), δ_(y2,p), δ_(y3,p), andδ_(y4,p).

At block 1520, the method 1500 corrects the peak locations for biaserror using a polynomial function of the peak location itself accordingto:

δ_(yn,p) ←aδ ² _(yn,p) +bδ _(yn,p) +c  (67)

where a, b, and c are the coefficients of the bias correction.

At block 1525, the method 1500 estimates the horizontal velocitycomponent v using Eqn. 53.

At block 1530, the method 1500 estimates the vertical velocity componentw using Eqn. 54, perhaps augmented by some other ambiguity resolutionmethod.

At block 1535, the method 1500 selects the velocity componentscalculated at blocks 1525 and 1530 to use as starting values of thevelocity components for the next block 1540 that are not subject toambiguity errors.

At block 1540, the method 1500 computes the interpolation parameters foreach acoustic beam corresponding to the latest estimates of velocitycomponents v and w using Eqns. 58-60. On the first iteration, theseestimates come from block 1535. On later iterations, they come fromblock 1550.

At block 1545, the method 1500 computes the phase for each acoustic beamusing Eqn. 51 with the interpolation parameters calculated at block1540.

At block 1550, the method 1500 uses the latest velocity components fromblock 1530 or block 1550 and the phases from block 1545 to computeimproved velocity estimates consistent with the phase measurements usingEqns. 61-63. The lateral velocity component u need not be computed usingEqn. 61 until iteration is complete because it is not needed in theinteration loop. In Eqn. 61, an estimate of J_(y) can be substituted forJ_(x).

Branch 1555 terminates the iteration of block 1510 when some measure ofconvergence is satisfied or after a fixed number of iterations.

FIG. 16 is a block diagram of a small aperture acoustic velocity sensor1600, according to an embodiment of the disclosed technology. The sensorincludes a plurality of transducer arrays 1610 that spatially modulateand project a plurality of acoustic beams in different directions. Thetransducer arrays 1610 receive and spatially demodulate a spatiotemporalpattern of acoustic signals corresponding to echoes of the projectedacoustic beams from a plurality of scatterers in the water whilepreserving the relative phase relationship of the backscattered acousticsignals. The transducer arrays 1610 may include elements of electronics1300, as described above with respect to FIG. 13, including arrays 1315and channel 1320 components, such as T/R switch 1325, analog front end1330, ADC 1335, beamformer 1340, IQ demod 1345 and filter 1350.

In certain embodiments, the transducer arrays 1610 include separateprojection arrays 1620 and hydrophone arrays 1630. For theseembodiments, the projection arrays 1620 spatially modulate and project aplurality of acoustic beams in different directions. For theseembodiments, the hydrophone arrays 1630 receive and spatially demodulatea spatiotemporal pattern of acoustic signals corresponding to echoes ofthe projected acoustic beams from a plurality of scatterers whilepreserving the relative phase relationship of the backscattered acousticsignals.

The small aperture acoustic velocity sensor 1600 includes a processor1640 configured to separate received acoustic signals backscattered fromdifferent projected acoustic beams, linearly combine the receivedacoustic signals over a portion of the hydrophone arrays, and measurevehicle velocity and/or water velocity components. The processor 1640may include the Doppler process 1360 described above with respect toFIG. 13. The small aperture acoustic velocity sensor 1600 includesmemory 1650 configured to store processing instructions, contral data,acoustic data, and/or intermediate or final results of the calculationsas described above with respect to FIGS. 14 and 15.

FIG. 17 is a flowchart of a process 1700 for measuring velocityaccording to an embodiment of the disclosed technology. At block 1710,the method 1700 spatially modulates and projects a plurality of acousticbeams from a plurality of sub-arrays in different directions. In anembodiment, at least some of the functionality of block 1710 may beperformed by the transducer arrays 1610 of FIG. 16, the projectionarrays 1620 of FIG. 16, and/or some or all of Array1-Array4 1315 of FIG.13.

At block 1720, the method 1700 receives and spatially demodulates aspatiotemporal pattern of acoustic signal corresponding to echoes of theprojected acoustic beams from a plurality of scatterers while preservingthe relative phase relationship of the back scattered acoustic signalsfrom the scatterers. In an embodiment, at least some of thefunctionality of block 1720 may be performed by the transducer arrays1610 of FIG. 16, the hydrophone arrays 1630 of FIG. 16, and/orArray1-Array4 1315 of FIG. 13.

At block 1730, the method 1700 separates the received acoustic signalsbackscattered from different projected acoustic beams. In an embodiment,at least some of the functionality of block 1730 may be performed by theprocessor 1640 of FIG. 16, and/or the Doppler processor 1360 of FIG. 13.

At block 1740, the method 1700 linearly combines the received acousticsignals. In an embodiment, at least some of the functionality of block1740 may be performed by the processor 1640 of FIG. 16, and/or theDoppler processor 1360 of FIG. 13.

At block 1750, the method 1700 measures vehicle velocity and/or watervelocity components, as described above with respect to FIGS. 14 and 15.In an embodiment, at least some of the functionality of block 1750 maybe performed by the processor 1640 of FIG. 16, and/or the Dopplerprocessor 1360 of FIG. 13.

Those skilled in the art will understand that information and signalsmay be represented using any of a variety of different technologies andtechniques. For example, data, instructions, commands, information,signals, bits, symbols, and chips that may be referenced throughout theabove description may be represented by voltages, currents,electromagnetic waves, magnetic fields or particles, optical fields orparticles, or any combination thereof.

Those skilled in the art will further appreciate that the variousillustrative logical blocks, modules, circuits, methods and algorithmsdescribed in connection with the examples disclosed herein may beimplemented as electronic hardware, computer software, or combinationsof both. To clearly illustrate this interchangeability of hardware andsoftware, various illustrative components, blocks, modules, circuits,methods and algorithms have been described above generally in terms oftheir functionality. Whether such functionality is implemented ashardware or software depends upon the particular application and designconstraints imposed on the overall system. Skilled artisans mayimplement the described functionality in varying ways for eachparticular application, but such implementation decisions should not beinterpreted as causing a departure from the scope of the presentinvention.

The various illustrative logical blocks, modules, and circuits describedin connection with the examples disclosed herein may be implemented orperformed with a general purpose processor, a digital signal processor(DSP), an application specific integrated circuit (ASIC), a fieldprogrammable gate array (FPGA) or other programmable logic device,discrete gate or transistor logic, discrete hardware components, or anycombination thereof designed to perform the functions described herein.A general-purpose processor may be a microprocessor, but in thealternative, the processor may be any conventional processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices, e.g., a combinationof a DSP and a microprocessor, a plurality of microprocessors, one ormore microprocessors in conjunction with a DSP core, or any other suchconfiguration.

The methods or algorithms described in connection with the examplesdisclosed herein may be embodied directly in hardware, in a softwaremodule executed by a processor, or in a combination of the two. Asoftware module may reside in RAM memory, flash memory, ROM memory,EPROM memory, EEPROM memory, registers, hard disk, a removable disk, aCD-ROM, or any other form of storage medium known in the art. A storagemedium may be connected to the processor such that the processor canread information from, and write information to, the storage medium. Inthe alternative, the storage medium may be integral to the processor.The processor and the storage medium may reside in an ASIC.

Depending on the embodiment, certain acts, events, or functions of anyof the methods described herein can be performed in a differentsequence, can be added, merged, or left out altogether (e.g., not alldescribed acts or events are necessary for the practice of the method).Moreover, in certain embodiments, acts or events can be performedconcurrently, rather than sequentially.

The previous description of the disclosed examples is provided to enableany person skilled in the art to make or use the present invention.Various modifications to these examples will be readily apparent tothose skilled in the art, and the generic principles defined herein maybe applied to other examples without departing from the spirit or scopeof the invention. As will be recognized, certain embodiments of theinventions described herein can be embodied within a form that does notprovide all of the features and benefits set forth herein, as somefeatures can be used or practiced separately from others. The scope ofcertain inventions disclosed herein is indicated by the appended claimsrather than by the foregoing description. All changes which come withinthe meaning and range of equivalency of the claims are to be embracedwithin their scope. Thus, the present invention is not intended to belimited to the examples shown herein but is to be accorded the widestscope consistent with the principles and novel features disclosedherein.

For purposes of summarizing the invention and the advantages achievedover the prior art, certain objects and advantages of the invention havebeen described herein above. Of course, it is to be understood that notnecessarily all such objects or advantages may be achieved in accordancewith any particular embodiment of the invention. Thus, for example,those skilled in the art will recognize that the invention may beembodied or carried out in a manner that achieves or optimizes oneadvantage or group of advantages as taught or suggested herein withoutnecessarily achieving other objects or advantages as may be taught orsuggested herein.

All of these embodiments are intended to be within the scope of theinvention herein disclosed. These and other embodiments will becomereadily apparent to those skilled in the art from the following detaileddescription of the preferred embodiments having reference to theattached figures, the invention not being limited to any particularpreferred embodiment(s) disclosed.

What is claimed is:
 1. A method of measuring velocity underwater usingan underwater active sonar system, the system comprising a plurality oftransducer arrays, each transducer array comprising a plurality ofsub-arrays, the transducer arrays configured to spatially modulate andproject a plurality of acoustic beams in different directions, receiveand spatially demodulate a spatiotemporal pattern of acoustic signalscorresponding to echoes of the projected acoustic beams from a pluralityof scatterers in the water while preserving the relative phaserelationship of the backscattered acoustic signals; the system furthercomprising a processor configured to separate received acoustic signalsbackscattered from different ones of the projected acoustic beams,linearly combine the received acoustic signals over a portion of thetransducer arrays, and measure vehicle velocity and/or water velocitycomponents based on the linearly combined signals, the methodcomprising: locating a bottom surface for each of the combined acousticsignals; selecting data segments in the combined acoustic signalsincluding echoes of the located bottom surface; computingauto-correlations of the selected data segments for each sub-array atzero time lag and at least one other lag at or near which the combinedacoustic signal repeats; computing cross-correlations of the selecteddata segments among the sub-arrays at zero time lag and at least oneother lag at or near which the combined acoustic signal repeats;estimating velocity to resolve phase ambiguity, comprising: computing acorrelation coefficient as a function of interpolation parameters;finding a peak of the correlation coefficient with respect to theinterpolation parameters; correcting the peak location for bias;estimating a horizontal velocity component; estimating a verticalvelocity component; and setting a velocity estimate based on theestimated horizontal and vertical velocity components; and computing thevelocity at or near an optimal interpolation point, comprising:computing interpolation parameters corresponding to the velocityestimate; calculating a phase at the peak location; and refining thevelocity estimate from the phase calculated at the peak location.
 2. Themethod of claim 1, further comprising applying beamforming processing soas to separate received acoustic signals.
 3. The method of claim 1,further comprising fitting a parametric model to the amplitude and phaseof an interference pattern of the received acoustic signals.
 4. A methodof measuring velocity underwater using an underwater active sonarsystem, the system comprising a plurality of transducer arrays, eachtransducer array comprising a plurality of sub-arrays, the transducerarrays configured to spatially modulate and project a plurality ofacoustic beams in different directions, receive and spatially demodulatea spatiotemporal pattern of acoustic signals corresponding to echoes ofthe projected acoustic beams from a plurality of scatterers in the waterwhile preserving the relative phase relationship of the backscatteredacoustic signals; the system further comprising a processor configuredto separate received acoustic signals backscattered from different onesof the projected acoustic beams, linearly combine the received acousticsignals over a portion of the transducer arrays, and measure vehiclevelocity and/or water velocity components in response to the linearlycombined signals, the method comprising: locating a bottom surface foreach of the combined acoustic signals; selecting data segments in thecombined acoustic signals including echoes of the located bottomsurface; computing auto-correlations of the selected data segments foreach sub-array at zero time lag and at least one other lag at or nearwhich the combined acoustic signal repeats; computing cross-correlationsof the selected data segments among the sub-arrays at zero time lag andat least one other lag at or near which the combined acoustic signalrepeats; estimating velocity to resolve phase ambiguity: and computingthe velocity at or near an optimal interpolation point.
 5. An underwateractive sonar system, comprising: a plurality of transducer arraysconfigured to spatially modulate and project a plurality of acousticbeams in different directions, receive and spatially demodulate aspatiotemporal pattern of acoustic signals corresponding to echoes ofthe projected acoustic beams from a plurality of scatterers whilepreserving the relative phase relationship of the backscattered acousticsignals; and a processor configured to separate received acousticsignals backscattered from different ones of the projected acousticbeams, linearly combine the received acoustic signals over a portion ofthe transducer arrays, and measure vehicle velocity and/or watervelocity components in response to the linearly combined signals.
 6. Thesystem of claim 5, wherein the processor is configured to applybeamforming processing to separate received acoustic signals.
 7. Thesystem of claim 5, wherein the processor is configured to fit aparametric model to the amplitude and phase of an interference patternof the received acoustic signals.
 8. The system of claim 5, wherein theprocessor is configured to measure vehicle velocity by backscatteringsound off the bottom surface of a body of water.
 9. The system of claim5, wherein the processor is configured to measure vehicle velocityand/or water velocity by processing backscattered acoustic signalsreceived from volume scatterers within a body of water.
 10. The systemof claim 5, wherein at least one of the transducer arrays projects agated monotone pulse to produce a narrowband signal.
 11. The system ofclaim 5, wherein at least one of the transducer arrays projects one ormore repetitions of a phase-coded or chirped signal to produce awideband signal.
 12. The system of claim 5, wherein the processor isconfigured to interpolate received acoustic signals, in at least one oftime and space, to approximate bistatic invariance and theDoppler-shifted pulse repetition interval.
 13. The system of claim 5,wherein the processor is configured to use the phase of across-correlation function at or near a lag equal to the Doppler-shiftedpulse repetition interval in multiple acoustic beams to measurevelocity.
 14. The system of claim 5, wherein each of the transducerarrays comprises at least one of a phased array, an array of phasedarrays, a multichannel array, a blazed array, an array of blazed arrays,and a set of piston transducers.
 15. The system of claim 5, wherein theshape of each of the transducer arrays is approximately polygonal, asection of a circle, or a section of an oval.
 16. The system of claim 5,wherein each transducer array comprises a plurality of sub-arrays. 17.An underwater active sonar system, comprising: a plurality of projectionarrays configured to spatially modulate and project a plurality ofacoustic beams in different directions; a plurality of hydrophone arraysconfigured to receive and spatially demodulate a spatiotemporal patternof acoustic signals corresponding to echoes of the projected acousticbeams from a plurality of scatterers in the water while preserving therelative phase relationship of the backscattered acoustic signals; and aprocessor configured to separate received acoustic signals backscatteredfrom different ones of the projected acoustic beams, linearly combinethe received acoustic signals over a portion of the hydrophone arrays,and measure vehicle velocity and/or water velocity components based onthe linearly combined signals.
 18. An underwater active sonar system,comprising: means for spatially modulating a plurality of acousticbeams; means for projecting the spatially modulated acoustic beams indifferent directions; means for receiving a spatiotemporal pattern ofacoustic signals corresponding to the echoes of projected acoustic beamsfrom a plurality of scatterers in the water while preserving therelative phase relationship of the backscattered acoustic signals; meansfor spatially demodulating the received spatiotemporal pattern ofacoustic signals; means for separating the received acoustic signalsbackscattered from different ones of the projected acoustic beams; meansfor linearly combining the separated received acoustic signals over aportion of the receiving means; and means for measuring vehicle velocityand/or water velocity components based on the linearly combined signals.